Depends on the fish. I had two large black mystery snails with my Dempsey, and he killed and ate one of them but leaves the other alone. He will kill and eat any snail I drop into the tank, regardless of size, but ignores that one snail that's already in there. Snails *are* part of a Jack Dempsey's natural diet, so I'd say it's definitely a gamble.
Any snail I drop in the tank that's small enough gets swallowed whole. The fish then crushes the entire shell with the throat teeth, then spits out the broken bits of shell and swallows the soft tissues. For larger snails, he either crushes the shell with his jaws and sucks the snail out of the opening, or grabs it and bashes it against rocks and driftwood to break the shell. He's a really determined snail eater.